Atomic clocks have been used for a time reference these days. The atomic clocks are also used in application fields that require high precision in time measurement. They use electromagnetic waves in a microwave range for frequency reference, which waves are produced through transitions between electronic levels in atoms such as Cs (caesium) and Rb (rubidium). For further precise measurement of time, devices called optical clocks have been developed.
The last few years have witnessed significant advances in optical clocks to reach uncertainties of 10−18 level in ion-based clocks and optical lattice clocks. Hitherto unexplored accuracy of optical clocks opens up new possibilities in science and technologies, such as probing new physics via possible variation of fundamental constants, and relativistic geodesy to measure gravitational potential differences. Evaluations of perturbations on the clock transitions are indeed at the heart of these endeavors.
Unperturbed transition frequencies have been accessed by extrapolating perturbations to zero, which is straight-forward if the correction is proportional to the perturber. Once the dependence becomes nonlinear, such as the blackbody radiation shift that changes as T4 with temperature, dedicated experimental and theoretical investigations are crucial. Contrarily, nonlinear response is leveraged to make the clock transition frequency insensitive to perturbations in hyper-Ramsey spectroscopy.